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Scaling the extrinsic curvature in the gravitational initial data: Generating trapped surfaces
Niall O'Murchadha
National University of Ireland, Cork
Abstract:
In the standard conformal method of constructing initial data for the Einstein equations, the `free' data is chosen to be a base Riemannian 3-metric and a divergenceless, tracefree tensor (TT) relative to this metric. One then gets a non-linear elliptic equation (the Lichnerowicz equation) for a conformal factor. If I take a TT tensor and multiply it by a constant, it is still TT. One can show that the conformal factor monotonically increases as this constant is increased. In particular, the ADM mass of the solution becomes unboundedly large. This forces the appearance of trapped surfaces in the intial data. This will be a `low-tech' talk, showing how one can prove interesting results using nothing but the maximum principle.
Thursday, June 2, 2011
11:00AM AP&M 5829
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Randolph E. Bank
Philip E. Gill
Michael Holst
Administrative Contact:
[ Click to Send Email ]
Niall O'Murchadha
National University of Ireland, Cork
Abstract:
In the standard conformal method of constructing initial data for the Einstein equations, the `free' data is chosen to be a base Riemannian 3-metric and a divergenceless, tracefree tensor (TT) relative to this metric. One then gets a non-linear elliptic equation (the Lichnerowicz equation) for a conformal factor. If I take a TT tensor and multiply it by a constant, it is still TT. One can show that the conformal factor monotonically increases as this constant is increased. In particular, the ADM mass of the solution becomes unboundedly large. This forces the appearance of trapped surfaces in the intial data. This will be a `low-tech' talk, showing how one can prove interesting results using nothing but the maximum principle.
Thursday, June 2, 2011
11:00AM AP&M 5829